Not unflipped normal but some faces are unusually brighter?
I figured it out. I had left some faces detached from the same-object mesh. How could I do that!
All I had do to was to merge vertices of the loose faces with the vertices in respected positions. The edges of the  loose faces were positioned just beside other edges of the larger mesh. So visually, there were two edges side by side. Merging vertices solved the problem.